JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Fluid Mechanics

The area of cross-section of a large tank is

0.5 m^{2}

. It has a narrow opening near the bottom having area of cross-section

1 cm^{2}

. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ______

cm s^{- 1}

.
[Take

g = 10 m s^{- 2}

]

Answer: 300

Solution

Apply Bernoulli's equation between the top surface and the opening. At the top, pressure is

P_{0} + \frac{m g}{A _{tank}}

and velocity is negligible. At the opening, pressure is

P_{0}

and velocity is

v

P_{0} + \frac{25 \times 10}{0.5} + ρ g h = P_{0} + \frac{1}{2} ρ v^{2}

where

h = 0.4

m and

ρ = 1000

kg/m³.

500 + 1000 \times 10 \times 0.4 = \frac{1}{2} \times 1000 \times v^{2}

500 + 4000 = 500 v^{2}

v^{2} = 9 ⟹ v = 3 m/s = 300 cm/s

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Integer answer

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JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Fluid Mechanics

Solution

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